Disparity in Learning

I am writing this post while thoroughly confused.  I need help.  The fate of many students hangs in the balance.

First, some background info.  At my school we do the math curriculum a little differently than most schools in Michigan.  Most schools teach in the following order: Algebra I, Geometry, Algebra II, and then either Pre-Calculus, or some other course like Statistics.  Most offer a fast-track like taking Algebra I in 8th grade, which after following the progression to Pre-Calculus, allows a student to take AP Calculus as a senior.

Every 8th grader at my school takes Algebra I.  Depending on the level of success, they are then placed in Algebra II or Algebra I again as freshmen.  To me it makes more sense to take Geometry immediately after Algebra I because the algebra needed to be successful in Geometry is of the Algebra variety.  So if students aren't that successful in Algebra I as 8th graders, most will take this track in Math: Algebra I, Algebra II, Geometry, and then Statistics.  However, when they get to me in Geometry as Juniors they are a full year, and sometimes 2 years removed from the kind of algebra we're using.  It's not hard, it's just been a while.  I have proposed changing to the typical track, but that is met with the question of whether freshmen could handle all of the heavy logic and reasoning skills that are also necessary in Geometry.

All of that being said, I have 2 sections of Geometry this year.  A class of 18 sophomores, who would have had success in 8th grade Alg. I, and a class of 12 juniors, who retook Alg. I as freshmen.

My problem is this:  My 18 sophomores are mostly girls and heavy duty type A personalities.  In some cases they have me convinced that the world is coming to an end if they get a B on something.  My juniors are more guys and more of the "meh" attitude.  It's totally fine to get a C or D, as long as they didn't have to put too much effort into it.  In some cases I identify more with the juniors because I had the same attitude in high school.  The only difference being that my lack of effort usually still ended up getting me an A anyway.  Hate me if you want, it's just the way it is.

I am torn between two seemingly logical positions with my situation.  Position 1 is that I should recognize that the junior class on average will simply not be able to handle the objectives to the same extent as the sophomore class.  Math has been an issue for them all along, and there's no reason to think that it will be any different this year.  Position 2 is that I should recognize the potential in each student regardless of their mathematical history.  Simplifying the objectives for the juniors is basically like lowering my expectations, which means I'm assuming they won't be able to handle it before they try.

There are pros and and cons to each position and it seems to me that I'm at an impasse.  This is my fourth year teaching Geometry, but it's the first year I've had 2 separate sections between sophomores and juniors. Last year they were all in one section, which had its own set of challenges and my first 2 years I had only sophomores, because the whole Algebra I split only started 3 years ago.

I am also struggling with how to apply the teachings of my faith to this situation, because usually whenever I'm stuck I just need to apply my faith, and then the correct choice naturally becomes apparent.  However, in this case it hasn't helped me much.  Jesus hung out with all of the sinners and basically cast out all the rich and righteous.  Instead of treating everyone equally, he turned the inequality on its head.  Can a really do that in a situation like this?  Can I justify spending more time with the weaker students and less with the strong?  If I do that, will I be able to handle feeling like I'm dropping the difficulty level so much that it's insulting to the weaker students?

I don't know the answers to these questions, but I'm mad that I can't seem to make a choice either way.

The Great Logarithm Battle Continues

I recently attended the St. Patrick High School graduation ceremony with a heavy heart.  One of my highest achieving students in math EVER, had just graduated and effectively removed himself from my sphere of influence with a mathematical misconception that would make lots of old, dead guys turn over in their graves.

We had just spent the better part of a whole school year arguing about which function was "better," the common logarithm (LOG), or the natural logarithm (ln).  To this day he still won't admit my mathematical dominance on the subject (probably out of spite), but I am unsure of whether he actually believes it or not.  I mean, his arguments are so feeble that I find it hard to believe he's actually being serious, but he debates with such passion, and with a sketchy little smile on his face, that I can't help but think he's just egging me on.  Well, either way I win, because I either have crushed him and his inferior claims, or he doesn't care at all so I win by default.

In any case, not that I expect this argument to ever end, but here are a few links that help support my side of the story.  It appears that the editors are scraping the bottom of the barrel for material on the common logarithm (not so common after all eh Joe?), but a plethora of material and applications for the natural logarithm are available.

Wikipedia Common Logarithm

Wikipedia Natural Logarithm

The fact that ln is graphically greater than log on the interval (1, infinity) and log is only graphically greater than ln on the interval (0, 1) only further lends credence to my impenetrable argument.

And all God's people said "Amen!"

The Math Mural has Arrived

Being a guy, a mathematician, and formerly a professional engineer has indeed limited my ability, passion, and motivation for decorating my room.  I've had comments from students and staff in years past that I need to spruce up my room a little bit (or a lot).  One comment that came from the MANS accreditation team last year was, "The Math Department bulletin boards are either boring or non-existent."  Well, now that it was officially on record that I was interior decoratingly challenged, I suppose I was accountable to fixing myself and my room up.  So this year, I made it my goal to make my room a little more inviting and personable, rather than the math dungeon that it had turned into.  I did the usual and ordered some posters and put up some decorations, but I had a hard time filling all of the space.  My room needed something more.

Coincidentally enough, I had the privilege of instructing a senior AP Calculus student this year who happens to be a very accomplished artist, and will be attending art school next year.  Part way through the year I realized that an excellent opportunity lay before me:  I could totally take advantage of her talents and commission her to paint a math mural over one of the bare spots on my wall!  What an EPIC idea!  On first mention, she thought it was a pretty sweet idea too, so we got to brainstorming.

The idea was to cover a bare spot with a tall window in the middle of it.  The general layout was to have Pi around the window, and then fill in the gaps with tons of mathematical know-how.  I left the creativity part up to her.  Well, the final result has been the talk of our little Catholic 100 student high school.  It's bright, colorful, and most importantly, chalk full of beautiful, mathematical truths.  Sigh.  Thanks for the amount of time and effort that went into this artwork Hannah.  You have truly left your mathematical mark on this school.  (And yes, that dragon is breathing mathematical fire.  You just can't see it from this distance)